The LF of other widely used LGNs can only be obtained by intractable
integration (marginalizing) over the hidden variables.
They must rely on a surrogate cost function in order to approximate LF training.
Examples are contrastive divergence (CD) to train restricted
Boltzmann machines [1]}, [2]}, and Kullback
Leibler divergence to train variational auto-encoder (VAE) [3]},
or an adversarial discriminative network to train generative adversarial networks
(GAN) [4]}. On the other hand, since the PBN generates data by manifold sampling, it
posesses a tractable likelihood function (LF) that allows direct gradient-based training.
